Trigonometric Identities

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97 Terms

1

cscθ

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2

secθ

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3

tanθ

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4

cotθ

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5

sin²θ

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6

cos²θ

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7

1

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8

cot²θ

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9

csc²θ

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10

sec²θ

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11

tan²θ

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12

sinθ

1/cscθ

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13

cosθ

1/secθ

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14

secθ reciprocal identity

1/cosθ

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15

cscθ reciprocal identity

1/sinθ

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16

cotθ reciprocal identity

1/tanθ

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17

tanθ quotient identity

sinθ/cosθ

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18

cotθ quotient identity

cosθ/sinθ

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19

-sinθ odd-even identity

sin(-θ)

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20

cosθ odd-even identity

cos(-θ)

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21

-tanθ odd-even identity

tan(-θ)

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22

-cscθ odd-even identity

csc(-θ)

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23

secθ odd-even identity

sec(-θ)

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24

-cotθ odd-even identity

cot(-θ)

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25

sinθ cofunction identity

cos (π/2-θ)

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26

cosθ cofunction identity

sin (π/2-θ)

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27

tanθ cofunction identity

cot (π/2-θ)

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28

cscθ cofunction identity

sec (π/2-θ)

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29

secθ cofunction identity

csc (π/2-θ)

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30

cotθ cofunction identity

tan (π/2-θ)

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31

sin²θ + cos²θ Pythagorean identity

1

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32

1 + tan²θ Pythagorean identity

sec²θ

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33

1 + cot²θ Pythagorean identity

csc²θ

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34

sin(α + β) sum identity

sinαcosβ + cosαsinβ

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35

sin(α - β) difference identity

sinαcosβ - cosαsinβ

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36

cos(α + β) sum identity

cosαcosβ - sinαsinβ

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37

cos(α - β) difference identity

cosαcosβ + sinαsinβ

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38

tan(α + β) sum identity

tanα + tanβ/1 - tanαtanβ

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39

tan(α - β) difference identity

tanα - tanβ/1 + tanαtanβ

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40

sin 2θ double-angle identity

2 sinθcosθ

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41

cos 2θ double-angle identity

cos²θ - sin²θ

2 cos²θ - 1

1 - 2 sin²θ

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42

tan 2θ double-angle identity

2 tanθ/1 - tan²θ

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43

sin½θ half-angle identity

±√1 - cosθ/2

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44

cos½θ half-angle identity

±√1 + cosθ/2

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45

tan½θ half-angle identity

±√1 - cosθ/1 + cosθ

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46

1/sin x

csc x

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47

1/cos x

sec x

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48

1/tan x

cot x

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49

1/csc x

sin x

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50

1/sec x

cos x

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51

1/cot x

tan x

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52

sin²x+cos²x

1

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53

1-cos²x

sin²x

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54

1-sin²x

cos²x

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55

1+tan²x

sec²x

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56

1+cot²x

csc²x

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57

sec²x-1

tan²x

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58

csc²x-1

cot²x

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59

sin(-x)

-sin x

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60

csc(-x)

-csc x

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61

cos(-x)

cos x

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62

sec(-x)

sec x

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63

tan(-x)

-tan x

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64

cot(-x)

-cot x

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65

sin(π/2-x)

cos x

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66

cos(π/2-x)

sin x

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67

tan(π/2-x)

cot x

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68

csc(π/2-x)

sec x

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69

sec(π/2-x)

csc x

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70

cot(π/2-x)

tan x

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71

sin x / cos x

tan x

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72

cos x/ sin x

cot x

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73

Identity (math)

A mathematical statement or equation that is true for any value.

<p>A mathematical statement or equation that is true for any value.</p>
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74

Pythagorean Identities

A trigonometric identity that is derived using the Pythagorean Theorem.

a² + b² = c²

x² + y² = r²

sin²θ + cos²θ = 1 (y=sin, x=cos, r=1 on unit circle)

1 + cot²θ = csc²θ (divide everything by sin²θ)

tan²θ + 1 = sec²θ (divide everything by cos²θ)

<p>A trigonometric identity that is derived using the Pythagorean Theorem.</p><p>a² + b² = c²</p><p>x² + y² = r²</p><p>sin²θ + cos²θ = 1 (y=sin, x=cos, r=1 on unit circle)</p><p>1 + cot²θ = csc²θ (divide everything by sin²θ)</p><p>tan²θ + 1 = sec²θ (divide everything by cos²θ)</p>
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75

Quotient

The answer to a division problem.

<p>The answer to a division problem.</p>
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Quotient Identities

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

<p>tanθ = sinθ/cosθ</p><p>cotθ = cosθ/sinθ</p>
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77

Reciprocal

One of a pair of numbers whose product is 1.

<p>One of a pair of numbers whose product is 1.</p>
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78

Reciprocal Identities

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79

Expression

A mathematical statement (variables,numbers, and operation symbols) that does not contain an equal sign.

<p>A mathematical statement (variables,numbers, and operation symbols) that does not contain an equal sign.</p>
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80

Equation

A mathematical statement that two expressions are equal.

<p>A mathematical statement that two expressions are equal.</p>
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81

Verify

To confirm or prove something is true.

<p>To confirm or prove something is true.</p>
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82

Simplify

To make something easier or less complicated.

<p>To make something easier or less complicated.</p>
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Solve

To find an answer to or explanation for a problem.

<p>To find an answer to or explanation for a problem.</p>
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84

Evaluate

For a specific input, find the numerical output of an function. Plug a number in to get a solution.

<p>For a specific input, find the numerical output of an function. Plug a number in to get a solution.</p>
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85

Isolate

To get a variable alone in a mathematical equation.

<p>To get a variable alone in a mathematical equation.</p>
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86

Factor (verb)

To find the factors of a number or expression.

<p>To find the factors of a number or expression.</p>
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87

Factor (noun)

A number which divides into another number exactly without leaving a remainder.

<p>A number which divides into another number exactly without leaving a remainder.</p>
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88

Distribute (Expand)

Multiplying each term inside the parentheses with the term outside of the parentheses.

<p>Multiplying each term inside the parentheses with the term outside of the parentheses.</p>
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89

Combine Like Terms

Simplifying an expression by using mathematical operations of terms with the same variables and exponents.

<p>Simplifying an expression by using mathematical operations of terms with the same variables and exponents.</p>
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90

Coefficient

A number multiplied by a variable in an algebraic expression.

<p>A number multiplied by a variable in an algebraic expression.</p>
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91

Variable

A letter or symbol used to represent numbers in Algebra.

<p>A letter or symbol used to represent numbers in Algebra.</p>
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92

Constant

A value that does not change.

<p>A value that does not change.</p>
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Radical

Another name for a root: one might refer to √2 as "radical 2."

<p>Another name for a root: one might refer to √2 as "radical 2."</p>
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Undefined

Having no solution.

(Examples: dividing by zero, negative square roots, the slope of a vertical line)

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95

Domain

All the possible x-values that can be input into a function.

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96

Range

All the possible y-values that can be the output of a function.

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Inverse Function

The function obtained by switching the domain (x) and range (y) in a function.

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